Using spherical harmonics to describe large-angle freeform lenses

We propose the use of spherical harmonics for large-angle freeform lenses as a dramatic improvement over polynomials set on the disk and plane, such as Zernike and X -Y polynomials. This new representation enables fitting of surfaces designed in spherical coordinates, such as freeform illumination lenses that would be impossible to describe with respect to a plane. The proposed representation is validated through an extremely compact, high-performance design.